Florida B.E.S.T. MA.912.GR.5.3
The Standard
Construct the inscribed and circumscribed circles of a triangle.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students locate two different triangle centers using precise compass and straightedge steps. They use those centers and correct radius lengths to draw circles through the vertices or tangent to the sides.
What Mastery Looks Like
- Students construct perpendicular bisectors to locate the circumcenter and angle bisectors to locate the incenter. Their outer circle passes through all three vertices, and their inner circle is tangent to all three sides.
Common Misconceptions
- Students often swap the incenter and circumcenter or use medians instead of bisectors. They may measure the incircle radius to a vertex rather than perpendicular to a side. They may also assume each center lies inside every triangle.
How to Assess It
- Give students a scalene triangle and ask them to construct both circles using a compass and straightedge. Require visible construction marks and labels for both centers.
Lesson moves
Ways to Teach It
Give pairs a compass, straightedge, and three triangle types to construct both centers and compare where each center falls.
Ask students to explain why perpendicular bisectors use vertex distances while angle bisectors lead to equal distances from the sides.
Run a center-matching game where students sort construction diagrams into incenter, circumcenter, incorrect bisectors, and incomplete construction.
Have students design a circular fountain inside a triangular plaza and a circular fence passing through the plaza’s three corners.
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Printable MA.912.GR.5.3 Worksheet
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Related Standards
- MA.912.GR.6.3
Solve mathematical problems involving triangles and quadrilaterals inscribed in a circle.
- MA.912.GR.5.4
Construct a regular polygon inscribed in a circle. Regular polygons are limited to triangles, quadrilaterals and hexagons.
- MA.8.GR.1.5
Solve problems involving the relationships of interior and exterior angles of a triangle.
- MA.912.T.1.4
Solve mathematical problems involving finding the area of a triangle given two sides and the included angle.
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